www.pudn.com > SolutionsforMultiuserDetection.rar > 4.3.rickard.ps

%!PS (but not EPSF; comments have been disabled)
%DVIPSCommandLine: dvips prob0403.dvi -o 4.3.rickard.ps
%DVIPSParameters: dpi=600, compressed, comments removed
%DVIPSSource:  TeX output 1999.03.11:0141
/TeXDict 250 dict def TeXDict begin /N{def}def /B{bind def}N /S{exch}N
/X{S N}B /TR{translate}N /isls false N /vsize 11 72 mul N /hsize 8.5 72
mul N /landplus90{false}def /@rigin{isls{[0 landplus90{1 -1}{-1 1}
ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale
isls{landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div
hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul
TR[matrix currentmatrix{dup dup round sub abs 0.00001 lt{round}if}
forall round exch round exch]setmatrix}N /@landscape{/isls true N}B
/@manualfeed{statusdict /manualfeed true put}B /@copies{/#copies X}B
/FMat[1 0 0 -1 0 0]N /FBB[0 0 0 0]N /nn 0 N /IE 0 N /ctr 0 N /df-tail{
/nn 8 dict N nn begin /FontType 3 N /FontMatrix fntrx N /FontBBox FBB N
string /base X array /BitMaps X /BuildChar{CharBuilder}N /Encoding IE N
end dup{/foo setfont}2 array copy cvx N load 0 nn put /ctr 0 N[}B /df{
/sf 1 N /fntrx FMat N df-tail}B /dfs{div /sf X /fntrx[sf 0 0 sf neg 0 0]
N df-tail}B /E{pop nn dup definefont setfont}B /ch-width{ch-data dup
length 5 sub get}B /ch-height{ch-data dup length 4 sub get}B /ch-xoff{
128 ch-data dup length 3 sub get sub}B /ch-yoff{ch-data dup length 2 sub
get 127 sub}B /ch-dx{ch-data dup length 1 sub get}B /ch-image{ch-data
dup type /stringtype ne{ctr get /ctr ctr 1 add N}if}B /id 0 N /rw 0 N
/rc 0 N /gp 0 N /cp 0 N /G 0 N /sf 0 N /CharBuilder{save 3 1 roll S dup
/base get 2 index get S /BitMaps get S get /ch-data X pop /ctr 0 N ch-dx
0 ch-xoff ch-yoff ch-height sub ch-xoff ch-width add ch-yoff
setcachedevice ch-width ch-height true[1 0 0 -1 -.1 ch-xoff sub ch-yoff
.1 sub]/id ch-image N /rw ch-width 7 add 8 idiv string N /rc 0 N /gp 0 N
/cp 0 N{rc 0 ne{rc 1 sub /rc X rw}{G}ifelse}imagemask restore}B /G{{id
gp get /gp gp 1 add N dup 18 mod S 18 idiv pl S get exec}loop}B /adv{cp
add /cp X}B /chg{rw cp id gp 4 index getinterval putinterval dup gp add
/gp X adv}B /nd{/cp 0 N rw exit}B /lsh{rw cp 2 copy get dup 0 eq{pop 1}{
dup 255 eq{pop 254}{dup dup add 255 and S 1 and or}ifelse}ifelse put 1
adv}B /rsh{rw cp 2 copy get dup 0 eq{pop 128}{dup 255 eq{pop 127}{dup 2
idiv S 128 and or}ifelse}ifelse put 1 adv}B /clr{rw cp 2 index string
putinterval adv}B /set{rw cp fillstr 0 4 index getinterval putinterval
adv}B /fillstr 18 string 0 1 17{2 copy 255 put pop}for N /pl[{adv 1 chg}
{adv 1 chg nd}{1 add chg}{1 add chg nd}{adv lsh}{adv lsh nd}{adv rsh}{
adv rsh nd}{1 add adv}{/rc X nd}{1 add set}{1 add clr}{adv 2 chg}{adv 2
chg nd}{pop nd}]dup{bind pop}forall N /D{/cc X dup type /stringtype ne{]
}if nn /base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{dup dup
length 1 sub dup 2 index S get sf div put}if put /ctr ctr 1 add N}B /I{
cc 1 add D}B /bop{userdict /bop-hook known{bop-hook}if /SI save N @rigin
0 0 moveto /V matrix currentmatrix dup 1 get dup mul exch 0 get dup mul
add .99 lt{/QV}{/RV}ifelse load def pop pop}N /eop{SI restore userdict
/eop-hook known{eop-hook}if showpage}N /@start{userdict /start-hook
known{start-hook}if pop /VResolution X /Resolution X 1000 div /DVImag X
/IE 256 array N 0 1 255{IE S 1 string dup 0 3 index put cvn put}for
65781.76 div /vsize X 65781.76 div /hsize X}N /p{show}N /RMat[1 0 0 -1 0
0]N /BDot 260 string N /rulex 0 N /ruley 0 N /v{/ruley X /rulex X V}B /V
{}B /RV statusdict begin /product where{pop product dup length 7 ge{0 7
getinterval dup(Display)eq exch 0 4 getinterval(NeXT)eq or}{pop false}
ifelse}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale rulex ruley false
RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR rulex ruley scale 1 1
false RMat{BDot}imagemask grestore}}ifelse B /QV{gsave newpath transform
round exch round exch itransform moveto rulex 0 rlineto 0 ruley neg
rlineto rulex neg 0 rlineto fill grestore}B /a{moveto}B /delta 0 N /tail
{dup /delta X 0 rmoveto}B /M{S p delta add tail}B /b{S p tail}B /c{-4 M}
B /d{-3 M}B /e{-2 M}B /f{-1 M}B /g{0 M}B /h{1 M}B /i{2 M}B /j{3 M}B /k{
4 M}B /w{0 rmoveto}B /l{p -4 w}B /m{p -3 w}B /n{p -2 w}B /o{p -1 w}B /q{
p 1 w}B /r{p 2 w}B /s{p 3 w}B /t{p 4 w}B /x{0 S rmoveto}B /y{3 2 roll p
a}B /bos{/SS save N}B /eos{SS restore}B end
TeXDict begin 40258431 52099146 1000 600 600 (prob0403.dvi)
@start /Fa 1 27 df<161E167EED01FE1507ED0FF8ED3FE0ED7FC0EDFF80913801FE00
4A5A4A5A5D140F4A5A5D143F5D147F92C7FCA25C5CB3B3B3A313015CA3495AA213075C49
5AA2495A495A137F49C8FC485A485AEA07F0EA1FE0485AB4C9FC12FCA2B4FCEA3FC06C7E
EA07F0EA03FC6C7E6C7E6D7E133F6D7E6D7EA26D7E801303A26D7EA3801300B3B3B3A380
80A281143F81141F816E7E1407816E7E6E7E913800FF80ED7FC0ED3FE0ED0FF8ED07FE15
01ED007E161E27C675823E>26 D E /Fb 7 107 df<007FB81280B912C0A26C17803204
799641>0 D<127012FCB4FCEA7FC0EA1FF0EA07FCEA01FF38007FC0EB1FF0EB07FCEB01
FF9038007FC0EC1FF0EC07FCEC01FF9138007FC0ED1FF0ED07FCED01FF9238007FC0EE1F
F0EE07FCEE01FF9338007FC0171F177F933801FF80933807FC00EE1FF0EE7FC04B48C7FC
ED07FCED1FF0ED7FC04A48C8FCEC07FCEC1FF0EC7FC04948C9FCEB07FCEB1FF0EB7FC048
48CAFCEA07FCEA1FF0EA7FC048CBFC12FC1270CCFCAD007FB81280B912C0A26C17803242
79B441>21 D<181EA4181F84A285180785727EA2727E727E85197E85F11F80F10FC0F107
F0007FBA12FCBCFCA26C19FCCCEA07F0F10FC0F11F80F13F00197E61614E5A4E5AA24E5A
61180F96C7FCA260181EA4482C7BAA53>33 D<0278151EA402F8151F4A81A20101834A15
0701038349486F7EA249486F7E49CA7E4983017E177E49834848EF1F804848EF0FC0D80F
E0EF07F0003FBA12FCBCFCA2003F19FCD80FE0CAEA07F0D803F0EF0FC06C6CEF1F806C6C
EF3F00017E177E6D5F6D5F6D6C4B5A6D6C4B5AA26D6C4B5A01015F6E150F010094C7FCA2
6E5D0278151EA4482C7BAA53>36 D102
D<12FCEAFFC0EA07F0EA01FCEA007E7F80131F80130FB3A7801307806D7E6D7EEB007EEC
1FF0EC07F8EC1FF0EC7E00495A495A495A5C130F5CB3A7131F5C133F91C7FC137E485AEA
07F0EAFFC000FCC8FC1D537ABD2A>I<126012F0B3B3B3B3A91260045377BD17>106
D E /Fc 2 51 df<13381378EA01F8121F12FE12E01200B3AB487EB512F8A215267BA521
>49 D<13FF000313E0380E03F0381800F848137C48137E00787F12FC6CEB1F80A4127CC7
FC15005C143E147E147C5C495A495A5C495A010EC7FC5B5B903870018013E0EA01803903
00030012065A001FB5FC5A485BB5FCA219267DA521>I E /Fd 8
122 df<15FE913803FF8091380F83E091383E01F091387C00F85C494813FC0103147C49
48137E5C130F495AA249C7FC16FE5B137EA2150113FE4914FCA20001140316F85BED07F0
1203ED0FE04914C0151F000715806DEB3F00157E6D5B390FEE01F09038E707E09038C3FF
80D9C0FCC7FC001F90C8FCA25BA2123FA290C9FCA25AA2127EA212FEA25AA2127027377E
A42B>26 D<121C127FEAFF80A5EA7F00121C0909798817>58 D<121C127FEAFF80A213C0
A3127F121C1200A412011380A2120313005A1206120E5A5A5A12600A19798817>II<124012F812FE6C7EEA3FE0EA0FF8EA03
FEC66C7EEB3FE0EB0FF8EB03FE903800FF80EC3FE0EC0FF8EC03FE913800FF80ED3FE0ED
0FF8ED03FE923800FF80EE3FE0EE0FF8EE03FE933800FF80EF3FC0A2EFFF80933803FE00
EE0FF8EE3FE0EEFF80DB03FEC7FCED0FF8ED3FE0EDFF80DA03FEC8FCEC0FF8EC3FE0ECFF
80D903FEC9FCEB0FF8EB3FE0EBFF80D803FECAFCEA0FF8EA3FE0EAFF8048CBFC12F81260
323279AD41>62 D<1760177017F01601A21603A21607160FA24C7EA216331673166316C3
A2ED0183A2ED0303150683150C160115181530A21560A215C014011580DA03007FA20206
1300140E140C5C021FB5FC5CA20260C7FC5C83495A8349C8FC1306A25BA25B13385B01F0
1680487E000716FFB56C013F13FF5EA2383C7DBB3E>65 D<133FEA1FFFA3C67E137EA313
FE5BA312015BA312035BA31207EBE0FCEBE3FF9038E707C0390FFE03E09038F801F001F0
13F8EBE000485A15FC5BA2123F90C7FCA214015A127EA2140312FE4814F8A2140715F05A
EC0FE0A215C0EC1F80143F00781400007C137E5C383C01F86C485A380F07C06CB4C7FCEA
01FC1E3B7CB924>98 D<13F8D803FE1470D8070F14F8000EEB8001121C12180038140300
3015F0EA701F1260013F130700E0010013E012C05BD8007E130F16C013FE5B151F000115
805BA2153F000315005BA25D157EA315FE5D1401000113033800F80790387C1FF8EB3FF9
EB0FE1EB00035DA2000E1307D83F805B007F495AA24A5A92C7FCEB003E007C5B00705B6C
485A381E07C06CB4C8FCEA01FC25367EA429>121 D E /Fe 47 123
df12 D<121C127FEAFF80A213C0A3127F121C1200A412011380A212
0313005A1206120E5A5A5A12600A1979B917>39 D<146014E0EB01C0EB0380EB0700130E
131E5B5BA25B485AA2485AA212075B120F90C7FCA25A121EA2123EA35AA65AB2127CA67E
A3121EA2121F7EA27F12077F1203A26C7EA26C7E1378A27F7F130E7FEB0380EB01C0EB00
E01460135278BD20>I<12C07E12707E7E7E120F6C7E6C7EA26C7E6C7EA21378A2137C13
3C133E131EA2131F7FA21480A3EB07C0A6EB03E0B2EB07C0A6EB0F80A31400A25B131EA2
133E133C137C1378A25BA2485A485AA2485A48C7FC120E5A5A5A5A5A13527CBD20>I<15
301578B3A6007FB812F8B912FCA26C17F8C80078C8FCB3A6153036367BAF41>43
D<121C127FEAFF80A213C0A3127F121C1200A412011380A2120313005A1206120E5A5A5A
12600A19798817>I<121C127FEAFF80A5EA7F00121C0909798817>46
D48 DIII<121C127FEA
FF80A5EA7F00121CC7FCB2121C127F5A1380A4127F121D1201A412031300A25A1206A212
0E5A121812385A1260093479A317>59 D<007FB812F8B912FCA3CCFCAEB912FCA36C17F8
36167B9F41>61 D<1538A3157CA315FEA34A7EA34A6C7EA202077FEC063FA2020E7FEC0C
1FA2021C7FEC180FA202387FEC3007A202707FEC6003A202C07F1501A2D901807F81A249
C77F167FA20106810107B6FCA24981010CC7121FA2496E7EA3496E7EA3496E7EA213E070
7E1201486C81D80FFC02071380B56C90B512FEA3373C7DBB3E>65
D69
DI73
D78
DI<003FB812E0A3D9C003EB001F273E0001FE130348EE01F00078160000701770A300
601730A400E01738481718A4C71600B3B0913807FF80011FB612E0A335397DB83C>84
D87 D<13101338137C13FE487E3803C7
80380783C0380F01E0381E00F04813780070131C48130E00401304170D77B92A>94
D97 DIIII<147E903803FF8090380FC1E0EB1F8790
383F0FF0137EA213FCA23901F803C091C7FCADB512FCA3D801F8C7FCB3AB487E387FFFF8
A31C3B7FBA19>IIII<
EA03F012FFA3120F1203B1913801FFFCA39138007FC01600157C15705D4A5A4A5A4AC7FC
141E1438147814FC13F1EBF3FEEBF73F01FE7FEBF81F496C7E8114076E7E6E7E81140015
7E157F811680ED1FC0486CEB3FF0B500C0B5FCA3283A7EB92C>107
DI<2703F00FF0EB1FE000
FFD93FFCEB7FF8913AF03F01E07E903BF1C01F83803F3D0FF3800FC7001F802603F70013
CE01FE14DC49D907F8EB0FC0A2495CA3495CB3A3486C496CEB1FE0B500C1B50083B5FCA3
40257EA445>I<3903F00FF000FFEB3FFCECF03F9039F1C01F803A0FF3800FC03803F700
13FE496D7EA25BA35BB3A3486C497EB500C1B51280A329257EA42E>I
I<3903F01FE000FFEB7FF89038F1E07E9039F3801F803A07F7000FC0D803FEEB07E049EB
03F04914F849130116FC150016FEA3167FAA16FEA3ED01FCA26DEB03F816F06D13076DEB
0FE001F614C09039F7803F009038F1E07E9038F0FFF8EC1FC091C8FCAB487EB512C0A328
357EA42E>II<3807E01F00FFEB7FC09038E1E3E09038E387F0380FE707EA03E613EE
9038EC03E09038FC0080491300A45BB3A2487EB512F0A31C257EA421>II<1318A51338A31378A313
F8120112031207001FB5FCB6FCA2D801F8C7FCB215C0A93800FC011580EB7C03017E1300
6D5AEB0FFEEB01F81A347FB220>IIIIII<003FB512FCA2EB8003D83E0013F8003CEB07
F00038EB0FE012300070EB1FC0EC3F800060137F150014FE495AA2C6485A495AA2495A49
5A495AA290387F000613FEA2485A485A0007140E5B4848130C4848131CA24848133C48C7
127C48EB03FC90B5FCA21F247EA325>I E /Ff 4 99 df40 D<12F07E127E7E6C7E6C7E6C7E7F6C7E6C7E12007F13
7F80133F806D7EA26D7EA26D7EA2801303A2801301A280A27F1580A4EC7FC0A615E0A214
3FAE147FA215C0A6ECFF80A415005BA25CA213035CA213075CA2495AA2495AA2495A5C13
7F91C7FC13FE5B1201485A485A5B485A485A48C8FC127E12F85A1B647ACA2C>I<903801
FFE0011F13FE017F6D7E48B612E03A03FE007FF84848EB1FFC6D6D7E486C6D7EA26F7FA3
6F7F6C5A6C5AEA00F090C7FCA40203B5FC91B6FC1307013F13F19038FFFC01000313E000
0F1380381FFE00485A5B127F5B12FF5BA35DA26D5B6C6C5B4B13F0D83FFE013EEBFFC03A
1FFF80FC7F0007EBFFF86CECE01FC66CEB8007D90FFCC9FC322F7DAD36>97
DI E /Fg 16 118 df46 D<913803FFC0023F13FC91
B6FC010315C0010F018113F0903A1FFC003FF849486D7E49486D7E49486D7E48496D1380
48496D13C0A24817E04890C813F0A34817F8A24817FC49157FA3007F17FEA600FF17FFB3
A5007F17FEA6003F17FCA26D15FFA26C17F8A36C17F0A26C6D4913E0A26C6D4913C06C17
806E5B6C6D4913006D6C495AD91FFCEB3FF8903A0FFF81FFF06D90B55A01011580D9003F
01FCC7FC020313C0384F7BCD43>48 D<91380FFFC091B512FC0107ECFF80011F15E09026
3FF8077F9026FF800113FC4848C76C7ED803F86E7E491680D807FC8048B416C080486D15
E0A4805CA36C17C06C5B6C90C75AD801FC1680C9FC4C13005FA24C5A4B5B4B5B4B13C04B
5BDBFFFEC7FC91B512F816E016FCEEFF80DA000713E0030113F89238007FFE707E701380
7013C018E07013F0A218F8A27013FCA218FEA2EA03E0EA0FF8487E487E487EB57EA318FC
A25E18F891C7FC6C17F0495C6C4816E001F04A13C06C484A1380D80FF84A13006CB44A5A
6CD9F0075BC690B612F06D5D011F1580010302FCC7FCD9001F1380374F7ACD43>51
D<177C17FEA2160116031607160FA2161F163F167FA216FF5D5DA25D5DED1FBFED3F3F15
3E157C15FCEC01F815F0EC03E01407EC0FC01580EC1F005C147E147C5C1301495A495A5C
495A131F49C7FC133E5B13FC485A5B485A1207485A485A90C8FC123E127E5ABA12C0A5C9
6C48C7FCAF020FB712C0A53A4F7CCE43>I80 D<91260FFF80130791B500F85B010702FF5B011F
EDC03F49EDF07F9026FFFC006D5A4801E0EB0FFD4801800101B5FC4848C87E4848814915
0F001F824981123F4981007F82A28412FF84A27FA26D82A27F7F6D93C7FC14C06C13F014
FF15F86CECFF8016FC6CEDFFC017F06C16FC6C16FF6C17C06C836C836D826D82010F8213
03010082021F16801400030F15C0ED007F040714E01600173F050F13F08383A200788200
F882A3187FA27EA219E07EA26CEFFFC0A27F6D4B13806D17006D5D01FC4B5A01FF4B5A02
C04A5A02F8EC7FF0903B1FFFC003FFE0486C90B65AD8FC0393C7FC48C66C14FC48010F14
F048D9007F90C8FC3C5479D24B>83 D98 D<913803FFC0023F13FC49B6FC010715
C04901817F903A3FFC007FF849486D7E49486D7E4849130F48496D7E48178048497F18C0
488191C7FC4817E0A248815B18F0A212FFA490B8FCA318E049CAFCA6127FA27F7EA218E0
6CEE01F06E14037E6C6DEC07E0A26C6DEC0FC06C6D141F6C6DEC3F806D6CECFF00D91FFE
EB03FE903A0FFFC03FF8010390B55A010015C0021F49C7FC020113F034387CB63D>101
D<137F497E000313E0487FA2487FA76C5BA26C5BC613806DC7FC90C8FCADEB3FF0B5FCA5
12017EB3B3A6B612E0A51B547BD325>105 D108 DII<913801
FFE0021F13FE91B612C0010315F0010F9038807FFC903A1FFC000FFED97FF86D6C7E4948
6D7F48496D7F48496D7F4A147F48834890C86C7EA24883A248486F7EA3007F1880A400FF
18C0AC007F1880A3003F18006D5DA26C5FA26C5F6E147F6C5F6C6D4A5A6C6D495B6C6D49
5B6D6C495BD93FFE011F90C7FC903A0FFF807FFC6D90B55A010015C0023F91C8FC020113
E03A387CB643>I<90397FE003FEB590380FFF80033F13E04B13F09238FE1FF89139E1F8
3FFC0003D9E3E013FEC6ECC07FECE78014EF150014EE02FEEB3FFC5CEE1FF8EE0FF04A90
C7FCA55CB3AAB612FCA52F367CB537>114 D<143EA6147EA414FEA21301A313031307A2
130F131F133F13FF5A000F90B6FCB8FCA426003FFEC8FCB3A9EE07C0AB011FEC0F8080A2
6DEC1F0015806DEBC03E6DEBF0FC6DEBFFF86D6C5B021F5B020313802A4D7ECB34>116
DI E /Fh 16 117 df<121EEA7F8012FF13C0A213E0A3
127FEA1E601200A413E013C0A312011380120313005A1206120E5A5A5A12600B1D78891B
>44 D<14FF010713E090381F81F890383E007C01FC133F4848EB1F8049130F4848EB07C0
4848EB03E0A2000F15F0491301001F15F8A2003F15FCA390C8FC4815FEA54815FFB3A46C
15FEA56D1301003F15FCA3001F15F8A26C6CEB03F0A36C6CEB07E0000315C06D130F6C6C
EB1F806C6CEB3F00013E137C90381F81F8903807FFE0010090C7FC28447CC131>48
D<143014F013011303131F13FFB5FC13E713071200B3B3B0497E497E007FB6FCA3204278
C131>I<14FF010713E0011F13F890387F80FC9038FC007E48487F4848EB1F804848EB0F
C0000FEC07E0485AED03F0485A16F8007F140190C713FCA25AA216FE1500A516FFA46C5C
A36C7E5D121F7F000F5C6C6C1306150E6C6C5B6C6C5BD8007C5B90383F01E090390FFF80
FE903801FE0090C8FC150116FCA4ED03F8A216F0D80F801307486C14E0486C130F16C0ED
1F80A249EB3F0049137E001EC75A001C495A000F495A3907E01FE06CB51280C649C7FCEB
1FF028447CC131>57 D77 D82
D<49B41303010FEBE007013F13F89039FE00FE0FD801F8131FD807E0EB079F49EB03DF48
486DB4FC48C8FC4881003E81127E82127C00FC81A282A37E82A27EA26C6C91C7FC7F7FEA
3FF813FE381FFFE06C13FE6CEBFFE06C14FC6C14FF6C15C0013F14F0010F80010180D900
1F7F14019138001FFF03031380816F13C0167F163F161F17E000C0150FA31607A37EA36C
16C0160F7E17806C151F6C16006C5D6D147ED8FBC05CD8F9F0495AD8F07C495A90393FC0
0FE0D8E00FB51280010149C7FC39C0003FF02B487BC536>I97 D99 D<167FED3FFFA315018182B3EC7F80903803FFF090380FC07C90383F000E017E13
07496D5AD803F87F48487F5B000F81485AA2485AA2127FA290C8FC5AAB7E7FA2123FA26C
7EA2000F5D7F6C6C5B00035C6C6C9038077F806C6C010E13C0013F011C13FE90380FC0F8
903803FFE09026007F0013002F467DC436>I104 DI
107 D111 D<3903F803F000FFEB1FFCEC3C
3EEC707F0007EBE0FF3803F9C000015B13FBEC007E153C01FF13005BA45BB3A748B4FCB5
12FEA3202C7DAB26>114 D<1306A5130EA4131EA3133E137EA213FE12011207001FB512
F0B6FCA2C648C7FCB3A4150CAA017E131C017F1318A26D133890381F8030ECC070903807
E0E0903801FFC09038007F001E3E7EBC26>116 D E /Fi 12 118
df68 D77 D<4AB47E020F13F8023F13FE9139FF007F80D903FCEB07E0D907
F0EB01F0D91FE0EB007849488049488049C87E48485D4915FF00034B138048485CA2485A
A2485AA2003F6F130049EC007C94C7FC127FA35B12FFAD127F7FA4123F7FA2001FEE01C0
7F000F16036D168012076C6C15076D160000015E6C6C151E6D6C5C6D6C5C6D6C5CD90FF8
495AD903FCEB07C0903A00FF803F8091263FFFFEC7FC020F13F80201138032417CBF3A>
99 D101
D<133C13FF487F487FA66C5B6C90C7FC133C90C8FCB3A2EB03C0EA07FF127FA41201EA00
7FA2133FB3B3AC497E497EB612E0A41B5F7DDE23>105 D108 D110 DI<9039078003F8D807FFEB0FFFB5013F13C092387C0FE091
3881F01F9238E03FF00001EB838039007F8700148FEB3F8E029CEB1FE0EE0FC00298EB03
0002B890C7FCA214B014F0A25CA55CB3B0497EEBFFF8B612FCA42C3F7CBE33>114
D<9139FFE00180010FEBFC03017FEBFF073A01FF001FCFD803F8EB03EFD807E0EB01FF48
487F4848147F48C8123F003E151F007E150F127CA200FC1507A316037EA27E7F6C7E6D91
C7FC13F8EA3FFE381FFFF06CEBFF806C14F86C14FF6C15C06C6C14F0011F80010714FED9
007F7F02031480DA003F13C01503030013E0167F00E0ED1FF0160F17F86C15071603A36C
1501A37EA26C16F016037E17E06D14076DEC0FC06D1580D8FDF0141FD8F8F8EC7F00013E
14FC3AF01FC00FF80107B512E0D8E001148027C0003FF8C7FC2D417DBF34>I<1438A714
78A414F8A31301A31303A21307130F131FA2137F13FF1203000F90B6FCB8FCA3260007F8
C8FCB3AE17E0AE6D6CEB01C0A316036D6C148016076D6C14006E6C5A91383FC01E91381F
F07C6EB45A020313E09138007F802B597FD733>II E end
TeXDict begin

1 0 bop 1373 289 a Fi(Multiuser)45 b(Detection)1656 530
y Fh(Scott)33 b(Ric)m(k)-5 b(ard)1619 725 y(Marc)m(h)33
b(10,)g(1999)515 1083 y Fg(Solution)45 b(to)h(Problem)f(4.03)515
1281 y Ff(\(a\))515 1434 y Fe(Note)27 b(that)h(in)g(the)g(expression,)
1390 1617 y Fd(A)1452 1629 y Fc(1)1489 1617 y Fd(y)1530
1629 y Fc(1)1567 1617 y Fd(b)1603 1629 y Fc(1)1658 1617
y Fe(+)18 b Fd(A)1803 1629 y Fc(2)1841 1617 y Fd(y)1882
1629 y Fc(2)1919 1617 y Fd(b)1955 1629 y Fc(2)2010 1617
y Fb(\000)g Fd(A)2155 1629 y Fc(1)2193 1617 y Fd(A)2255
1629 y Fc(2)2292 1617 y Fd(\032b)2371 1629 y Fc(1)2408
1617 y Fd(b)2444 1629 y Fc(2)2481 1617 y Fd(;)515 1800
y Fe(w)n(e)37 b(can)h(alw)n(a)n(ys)e(c)n(ho)r(ose)h Fd(b)1396
1812 y Fc(1)1471 1800 y Fe(and)h Fd(b)1679 1812 y Fc(2)1754
1800 y Fe(to)g(mak)n(e)f(an)n(y)g(t)n(w)n(o)h(terms)f(\(of)i(the)f
(three\))g(ha)n(v)n(e)515 1899 y(p)r(ositiv)n(e)i(sign.)78
b(The)41 b(third)g(term's)g(sign)g(is)g(then)g(constrained.)77
b(W)-7 b(e)41 b(use)g(this)h(fact)515 1999 y(throughout)27
b(the)h(solution.)639 2098 y(If,)1383 2198 y(min)q Fb(f)p
Fd(A)1626 2210 y Fc(1)1663 2198 y Fb(j)p Fd(y)1727 2210
y Fc(1)1764 2198 y Fb(j)p Fd(;)14 b(A)1886 2210 y Fc(2)1923
2198 y Fb(j)p Fd(y)1987 2210 y Fc(2)2024 2198 y Fb(jg)23
b(\025)f Fd(A)2261 2210 y Fc(1)2299 2198 y Fd(A)2361
2210 y Fc(2)2398 2198 y Fb(j)p Fd(\032)p Fb(j)p Fd(;)515
2348 y Fe(then)28 b(clearly)-7 b(,)1375 2447 y(max)p
Fb(f)p Fd(A)1634 2459 y Fc(1)1671 2447 y Fb(j)p Fd(y)1735
2459 y Fc(1)1772 2447 y Fb(j)p Fd(;)14 b(A)1894 2459
y Fc(2)1931 2447 y Fb(j)p Fd(y)1995 2459 y Fc(2)2032
2447 y Fb(jg)23 b(\025)f Fd(A)2269 2459 y Fc(1)2307 2447
y Fd(A)2369 2459 y Fc(2)2406 2447 y Fb(j)p Fd(\032)p
Fb(j)p Fd(;)515 2597 y Fe(so)j(w)n(e)i(should)f(c)n(ho)r(ose)f(\()p
Fd(b)1329 2609 y Fc(1)1366 2597 y Fd(;)14 b(b)1439 2609
y Fc(2)1476 2597 y Fe(\))27 b(so)e(that)i Fd(A)1876 2609
y Fc(1)1913 2597 y Fd(y)1954 2609 y Fc(1)1991 2597 y
Fd(b)2027 2609 y Fc(1)2091 2597 y Fe(and)f Fd(A)2313
2609 y Fc(2)2351 2597 y Fd(y)2392 2609 y Fc(2)2428 2597
y Fd(b)2464 2609 y Fc(2)2528 2597 y Fe(are)f(b)r(oth)i(p)r(ositiv)n(e.)
36 b(That)515 2696 y(is,)1649 2857 y(^)1652 2879 y Fd(b)1688
2891 y Fc(1)1808 2879 y Fe(=)83 b(sgn)o(\()p Fd(y)2149
2891 y Fc(1)2186 2879 y Fe(\))1649 2991 y(^)1652 3012
y Fd(b)1688 3024 y Fc(2)1808 3012 y Fe(=)g(sgn)o(\()p
Fd(y)2149 3024 y Fc(2)2186 3012 y Fe(\))p Fd(:)639 3195
y Fe(Otherwise,)27 b(if,)1383 3295 y(min)q Fb(f)p Fd(A)1626
3307 y Fc(1)1663 3295 y Fb(j)p Fd(y)1727 3307 y Fc(1)1764
3295 y Fb(j)p Fd(;)14 b(A)1886 3307 y Fc(2)1923 3295
y Fb(j)p Fd(y)1987 3307 y Fc(2)2024 3295 y Fb(jg)23 b
Fd(<)f(A)2261 3307 y Fc(1)2299 3295 y Fd(A)2361 3307
y Fc(2)2398 3295 y Fb(j)p Fd(\032)p Fb(j)p Fd(;)515 3444
y Fe(then)d(w)n(e)f(should)g(c)n(ho)r(ose)f(\()p Fd(b)1384
3456 y Fc(1)1421 3444 y Fd(;)d(b)1494 3456 y Fc(2)1531
3444 y Fe(\))19 b(so)e(that)i Fb(\000)p Fd(A)1972 3456
y Fc(1)2009 3444 y Fd(A)2071 3456 y Fc(2)2109 3444 y
Fd(\032b)2188 3456 y Fc(1)2224 3444 y Fd(b)2260 3456
y Fc(2)2316 3444 y Fe(and)f(the)h(larger)d(of)i(\()p
Fd(A)3007 3456 y Fc(1)3045 3444 y Fd(y)3086 3456 y Fc(1)3123
3444 y Fd(b)3159 3456 y Fc(1)3196 3444 y Fd(;)c(A)3295
3456 y Fc(2)3332 3444 y Fd(y)3373 3456 y Fc(2)3410 3444
y Fd(b)3446 3456 y Fc(2)3483 3444 y Fe(\))515 3544 y(ha)n(v)n(e)26
b(p)r(ositiv)n(e)h(sign.)37 b(If)28 b Fd(A)1362 3556
y Fc(1)1399 3544 y Fb(j)p Fd(y)1463 3556 y Fc(1)1500
3544 y Fb(j)23 b(\025)g Fd(A)1696 3556 y Fc(2)1734 3544
y Fb(j)p Fd(y)1798 3556 y Fc(2)1835 3544 y Fb(j)p Fe(,)k(w)n(e)h(ha)n
(v)n(e,)1357 3713 y(^)1360 3735 y Fd(b)1396 3747 y Fc(1)1516
3735 y Fe(=)83 b(sgn)o(\()p Fd(y)1857 3747 y Fc(1)1894
3735 y Fe(\))1357 3847 y(^)1360 3869 y Fd(b)1396 3881
y Fc(2)1516 3869 y Fe(=)g(sgn)o(\()p Fb(\000)p Fd(\032b)1960
3881 y Fc(1)1997 3869 y Fe(\))23 b(=)g(sgn)o(\()p Fb(\000)p
Fd(\032y)2441 3881 y Fc(1)2478 3869 y Fe(\))p Fd(;)515
4052 y Fe(and)k(if)h Fd(A)814 4064 y Fc(1)852 4052 y
Fb(j)p Fd(y)916 4064 y Fc(1)953 4052 y Fb(j)23 b Fd(<)g(A)1149
4064 y Fc(2)1186 4052 y Fb(j)p Fd(y)1250 4064 y Fc(2)1287
4052 y Fb(j)p Fe(,)28 b(w)n(e)f(ha)n(v)n(e,)1357 4221
y(^)1360 4243 y Fd(b)1396 4255 y Fc(2)1516 4243 y Fe(=)83
b(sgn)o(\()p Fd(y)1857 4255 y Fc(2)1894 4243 y Fe(\))1357
4355 y(^)1360 4377 y Fd(b)1396 4389 y Fc(1)1516 4377
y Fe(=)g(sgn)o(\()p Fb(\000)p Fd(\032b)1960 4389 y Fc(2)1997
4377 y Fe(\))23 b(=)g(sgn)o(\()p Fb(\000)p Fd(\032y)2441
4389 y Fc(2)2478 4377 y Fe(\))p Fd(:)515 4559 y Fe(W)-7
b(e)28 b(can)f(com)n(bine)g(these)h(t)n(w)n(o)f(cases)f(in)n(to)h(one)h
(using,)690 4765 y(^)693 4787 y Fd(b)729 4799 y Fc(1)849
4787 y Fe(=)83 b(sgn)o(\()p Fd(A)1211 4799 y Fc(1)1249
4787 y Fd(y)1290 4799 y Fc(1)1345 4787 y Fb(\000)18 b
Fe(sgn\()p Fd(\032)p Fe(\))p Fd(A)1718 4799 y Fc(2)1756
4787 y Fd(y)1797 4799 y Fc(2)1833 4787 y Fe(\))24 b(=)1976
4670 y Fa(\032)2134 4737 y Fe(sgn)o(\()p Fd(y)2327 4749
y Fc(1)2365 4737 y Fe(\))k(if)g Fd(A)2563 4749 y Fc(1)2600
4737 y Fb(j)p Fd(y)2664 4749 y Fc(1)2701 4737 y Fb(j)23
b(\025)g Fd(A)2897 4749 y Fc(2)2934 4737 y Fb(j)p Fd(y)2998
4749 y Fc(2)3035 4737 y Fb(j)2080 4836 y Fe(sgn\()p Fb(\000)p
Fd(\032y)2382 4848 y Fc(2)2418 4836 y Fe(\))28 b(if)g
Fd(A)2616 4848 y Fc(1)2654 4836 y Fb(j)p Fd(y)2718 4848
y Fc(1)2755 4836 y Fb(j)23 b Fd(<)g(A)2951 4848 y Fc(2)2988
4836 y Fb(j)p Fd(y)3052 4848 y Fc(2)3089 4836 y Fb(j)690
4998 y Fe(^)693 5020 y Fd(b)729 5032 y Fc(2)849 5020
y Fe(=)83 b(sgn)o(\()p Fd(A)1211 5032 y Fc(2)1249 5020
y Fd(y)1290 5032 y Fc(2)1345 5020 y Fb(\000)18 b Fe(sgn\()p
Fd(\032)p Fe(\))p Fd(A)1718 5032 y Fc(1)1756 5020 y Fd(y)1797
5032 y Fc(1)1833 5020 y Fe(\))24 b(=)1976 4903 y Fa(\032)2080
4969 y Fe(sgn\()p Fb(\000)p Fd(\032y)2382 4981 y Fc(1)2418
4969 y Fe(\))k(if)g Fd(A)2616 4981 y Fc(1)2654 4969 y
Fb(j)p Fd(y)2718 4981 y Fc(1)2755 4969 y Fb(j)23 b(\025)g
Fd(A)2951 4981 y Fc(2)2988 4969 y Fb(j)p Fd(y)3052 4981
y Fc(2)3089 4969 y Fb(j)2134 5069 y Fe(sgn)o(\()p Fd(y)2327
5081 y Fc(2)2365 5069 y Fe(\))28 b(if)g Fd(A)2563 5081
y Fc(1)2600 5069 y Fb(j)p Fd(y)2664 5081 y Fc(1)2701
5069 y Fb(j)23 b Fd(<)g(A)2897 5081 y Fc(2)2934 5069
y Fb(j)p Fd(y)2998 5081 y Fc(2)3035 5069 y Fb(j)3178
5020 y Fd(:)1926 5506 y Fe(1)p eop
2 1 bop 515 -60 a Ff(\(b\))515 107 y Fe(First)34 b(note)h(that)g(b)n(y)
g(symmetry)f(w)n(e)h(need)g(only)f(deriv)n(e)g(the)h(general)f(form)n
(ula)g(for)3280 85 y(^)3283 107 y Fd(b)3319 119 y Fc(1)3356
107 y Fe(;)515 206 y(sw)n(apping)26 b(the)i(1)23 b Fb($)g
Fe(2)k(will)h(yield)g(the)g(form)n(ula)e(for)2189 184
y(^)2192 206 y Fd(b)2228 218 y Fc(2)2265 206 y Fe(.)639
306 y(If)d Fd(A)779 318 y Fc(1)817 306 y Fb(j)p Fd(y)881
318 y Fc(1)918 306 y Fb(j)g Fe(is)f(the)h(minimal)g(\(magnitude\))g
(term,)h(then)f Fd(b)2406 318 y Fc(1)2466 306 y Fe(should)f(b)r(e)i(c)n
(hosen)d(to)i(mak)n(e)515 405 y Fb(\000)p Fd(A)642 417
y Fc(1)679 405 y Fd(A)741 417 y Fc(2)778 405 y Fd(\032b)857
417 y Fc(1)894 405 y Fd(b)930 417 y Fc(2)1002 405 y Fe(p)r(ositiv)n(e.)
58 b(In)34 b(this)h(case,)h Fd(b)1886 417 y Fc(2)1958
405 y Fe(will)f(ha)n(v)n(e)e(b)r(een)i(c)n(hosen)f(to)h(mak)n(e)f
Fd(A)3191 417 y Fc(2)3228 405 y Fd(y)3269 417 y Fc(2)3306
405 y Fd(b)3342 417 y Fc(2)515 505 y Fe(p)r(ositiv)n(e,)27
b(that)h(is,)1128 483 y(^)1131 505 y Fd(b)1167 517 y
Fc(2)1227 505 y Fe(=)23 b(sgn)o(\()p Fd(y)1508 517 y
Fc(2)1546 505 y Fe(\).)37 b(Th)n(us,)1223 675 y(^)1226
697 y Fd(b)1262 709 y Fc(1)1322 697 y Fe(=)22 b(sgn\()p
Fb(\000)p Fd(A)1689 709 y Fc(1)1726 697 y Fd(A)1788 709
y Fc(2)1826 697 y Fd(\032)p Fe(sgn)o(\()p Fd(y)2062 709
y Fc(2)2099 697 y Fe(\)\))i(=)e(sgn\()p Fb(\000)p Fd(\032y)2576
709 y Fc(2)2613 697 y Fe(\))p Fd(:)515 879 y Fe(On)27
b(the)h(other)f(hand,)h(if)g Fd(A)1382 891 y Fc(1)1419
879 y Fb(j)p Fd(y)1483 891 y Fc(1)1520 879 y Fb(j)g Fe(is)g(not)f(the)h
(minimal)g(\(magnitude\))g(term,)g(then,)1721 1049 y(^)1724
1071 y Fd(b)1760 1083 y Fc(1)1820 1071 y Fe(=)22 b(sgn\()p
Fd(y)2101 1083 y Fc(1)2138 1071 y Fe(\))515 1254 y(T)-7
b(o)27 b(summarize,)g(w)n(e)g(ha)n(v)n(e)f(the)i(follo)n(wing)f
(conditions,)1230 1436 y Fd(A)1292 1448 y Fc(1)1329 1436
y Fb(j)p Fd(y)1393 1448 y Fc(1)1430 1436 y Fb(j)h Fe(minimal)51
b Fb(\000)-14 b(!)1981 1414 y Fe(^)1984 1436 y Fd(b)2020
1448 y Fc(1)2080 1436 y Fe(=)22 b(sgn\()p Fb(\000)p Fd(\032y)2469
1448 y Fc(2)2506 1436 y Fe(\))735 b(\(1\))1190 1570 y
Fd(A)1252 1582 y Fc(1)1289 1570 y Fb(j)p Fd(y)1353 1582
y Fc(1)1390 1570 y Fb(j)28 b Fe(not)g(minimal)51 b Fb(\000)-15
b(!)2088 1548 y Fe(^)2091 1570 y Fd(b)2127 1582 y Fc(1)2187
1570 y Fe(=)23 b(sgn)o(\()p Fd(y)2468 1582 y Fc(1)2506
1570 y Fe(\))735 b(\(2\))639 1753 y(No)n(w)27 b(consider)g(the)h(form)n
(ula,)929 1948 y(^)932 1970 y Fd(b)968 1982 y Fc(1)1028
1970 y Fe(=)23 b(sgn)o(\()p Fd(A)1330 1982 y Fc(1)1368
1970 y Fd(y)1409 1982 y Fc(1)1465 1970 y Fe(+)1558 1913
y(1)p 1558 1951 42 4 v 1558 2027 a(2)1609 1970 y Fb(j)p
Fd(A)1694 1982 y Fc(2)1732 1970 y Fd(y)1773 1982 y Fc(2)1828
1970 y Fb(\000)18 b Fd(A)1973 1982 y Fc(1)2011 1970 y
Fd(A)2073 1982 y Fc(2)2110 1970 y Fd(\032)p Fb(j)g(\000)2287
1913 y Fe(1)p 2287 1951 V 2287 2027 a(2)2339 1970 y Fb(j)p
Fd(A)2424 1982 y Fc(2)2462 1970 y Fd(y)2503 1982 y Fc(2)2558
1970 y Fe(+)g Fd(A)2703 1982 y Fc(1)2740 1970 y Fd(A)2802
1982 y Fc(2)2840 1970 y Fd(\032)p Fb(j)p Fe(\))p Fd(:)312
b Fe(\(3\))515 2176 y(W)-7 b(e)25 b(endea)n(v)n(or)e(to)i(sho)n(w)g
(Equation)f(3)h(satis\014es)f(conditions)h(1)g(and)g(2.)35
b(In)26 b(the)f(case)g(where)515 2275 y Fd(A)577 2287
y Fc(1)614 2275 y Fb(j)p Fd(y)678 2287 y Fc(1)715 2275
y Fb(j)33 b Fe(is)g(the)g(minimal)g(\(magnitude\))h(term,)g(w)n(e)e
(consider)g(the)h(four)g(p)r(ossibilities)g(for)515 2375
y(the)40 b(signs)f(of)h(the)g Fd(A)1210 2387 y Fc(2)1247
2375 y Fd(y)1288 2387 y Fc(2)1352 2375 y Fb(\000)26 b
Fd(A)1505 2387 y Fc(1)1543 2375 y Fd(A)1605 2387 y Fc(2)1642
2375 y Fd(\032)40 b Fe(and)g Fd(A)1961 2387 y Fc(2)1998
2375 y Fd(y)2039 2387 y Fc(2)2103 2375 y Fe(+)26 b Fd(A)2256
2387 y Fc(1)2293 2375 y Fd(A)2355 2387 y Fc(2)2393 2375
y Fd(\032)40 b Fe(terms.)73 b(F)-7 b(or)39 b(example,)k(If,)515
2474 y Fd(A)577 2486 y Fc(2)614 2474 y Fd(y)655 2486
y Fc(2)718 2474 y Fb(\000)26 b Fd(A)871 2486 y Fc(1)908
2474 y Fd(A)970 2486 y Fc(2)1008 2474 y Fd(\032)38 b
Fe(and)h Fd(A)1324 2486 y Fc(2)1361 2474 y Fd(y)1402
2486 y Fc(2)1465 2474 y Fe(+)26 b Fd(A)1618 2486 y Fc(1)1655
2474 y Fd(A)1717 2486 y Fc(2)1755 2474 y Fd(\032)38 b
Fe(are)g(b)r(oth)h(p)r(ositiv)n(e,)i(then)2735 2453 y(^)2738
2474 y Fd(b)2774 2486 y Fc(1)2852 2474 y Fe(=)g(sgn\()p
Fd(A)3173 2486 y Fc(1)3211 2474 y Fd(y)3252 2486 y Fc(1)3314
2474 y Fb(\000)515 2574 y Fd(A)577 2586 y Fc(1)614 2574
y Fd(A)676 2586 y Fc(2)714 2574 y Fd(\032)p Fe(\))23
b(=)g(sgn)o(\()p Fb(\000)p Fd(\032)p Fe(\).)35 b(Additionally)-7
b(,)22 b(w)n(e)f(kno)n(w)f(for)g(b)r(oth)h(terms)g(to)g(b)r(e)g(p)r
(ositiv)n(e,)h Fd(y)3167 2586 y Fc(2)3227 2574 y Fd(>)g
Fe(0.)515 2674 y(Th)n(us,)28 b(in)h(this)g(case,)f(w)n(e)g(can)g
(include)h(a)f Fd(y)1884 2686 y Fc(2)1949 2674 y Fe(in)h(the)g(form)n
(ula,)f(sgn)o(\()p Fb(\000)p Fd(\032y)2821 2686 y Fc(2)2858
2674 y Fe(\).)40 b(A)29 b(summary)515 2773 y(for)g(all)h(p)r(ossible)f
(cases)g(of)h(\(sgn\()p Fd(A)1631 2785 y Fc(2)1668 2773
y Fd(y)1709 2785 y Fc(2)1766 2773 y Fb(\000)20 b Fd(A)1913
2785 y Fc(1)1950 2773 y Fd(A)2012 2785 y Fc(2)2050 2773
y Fd(\032)p Fe(\))p Fd(;)14 b Fe(sgn)o(\()p Fd(A)2376
2785 y Fc(2)2414 2773 y Fd(y)2455 2785 y Fc(2)2512 2773
y Fe(+)20 b Fd(A)2659 2785 y Fc(1)2696 2773 y Fd(A)2758
2785 y Fc(2)2796 2773 y Fd(\032)p Fe(\)\),)31 b(follo)n(wing)e(in)515
2873 y(a)e(similar)g(fashion)g(is)g(listed)h(here.)p
1168 2976 1558 4 v 1166 3085 4 110 v 1259 3055 a(case)p
1497 3085 V 1673 3034 a(^)1676 3055 y Fd(b)1712 3067
y Fc(1)p 1924 3085 V 2022 3055 a Fe(fact)p 2254 3085
V 2451 3034 a(^)2454 3055 y Fd(b)2490 3067 y Fc(1)p 2724
3085 V 1168 3089 1558 4 v 1168 3105 V 1166 3205 4 100
v 1218 3175 a Fe(\(+)p Fd(;)14 b Fe(+\))p 1497 3205 V
117 w(sgn)o(\()p Fb(\000)p Fd(\032)p Fe(\))p 1924 3205
V 117 w Fd(y)2016 3187 y Fc(2)2076 3175 y Fd(>)23 b Fe(0)p
2254 3205 V 99 w(sgn\()p Fb(\000)p Fd(\032y)2607 3187
y Fc(2)2643 3175 y Fe(\))p 2724 3205 V 1168 3208 1558
4 v 1166 3308 4 100 v 1218 3278 a(\()p Fb(\000)p Fd(;)14
b Fb(\000)p Fe(\))p 1497 3308 V 149 w(sgn\()p Fd(\032)p
Fe(\))p 1924 3308 V 149 w Fd(y)2016 3290 y Fc(2)2076
3278 y Fd(<)23 b Fe(0)p 2254 3308 V 99 w(sgn\()p Fb(\000)p
Fd(\032y)2607 3290 y Fc(2)2643 3278 y Fe(\))p 2724 3308
V 1168 3311 1558 4 v 1166 3411 4 100 v 1218 3381 a(\(+)p
Fd(;)14 b Fb(\000)p Fe(\))p 1497 3411 V 132 w(sgn)o(\()p
Fd(y)1774 3393 y Fc(2)1811 3381 y Fe(\))p 1924 3411 V
150 w Fd(\032)23 b(<)g Fe(0)p 2254 3411 V 116 w(sgn\()p
Fb(\000)p Fd(\032y)2607 3393 y Fc(2)2643 3381 y Fe(\))p
2724 3411 V 1168 3414 1558 4 v 1166 3514 4 100 v 1218
3484 a(\()p Fb(\000)p Fd(;)14 b Fe(+\))p 1497 3514 V
99 w(sgn\()p Fb(\000)p Fd(y)1807 3496 y Fc(2)1844 3484
y Fe(\))p 1924 3514 V 117 w Fd(\032)23 b(>)g Fe(0)p 2254
3514 V 116 w(sgn\()p Fb(\000)p Fd(\032y)2607 3496 y Fc(2)2643
3484 y Fe(\))p 2724 3514 V 1168 3517 1558 4 v 639 3716
a(Th)n(us,)28 b(Equation)e(3)h(satis\014es)g(condition)h(1.)639
3816 y(If)38 b Fd(A)794 3828 y Fc(1)832 3816 y Fb(j)p
Fd(y)896 3828 y Fc(1)933 3816 y Fb(j)f Fe(is)g(not)h(minimal,)i(then)e
(w)n(e)f(can)g(again)f(follo)n(w)h(a)g(similar)f(approac)n(h)g(as)515
3916 y(ab)r(o)n(v)n(e)26 b(to)h(pro)r(duce)h(the)g(follo)n(wing.)p
801 4035 2293 4 v 799 4144 4 110 v 892 4114 a(case)p
1129 4144 V 1494 4092 a(^)1497 4114 y Fd(b)1533 4126
y Fc(1)p 1935 4144 V 2265 4114 a Fe(fact)p 2729 4144
V 2872 4092 a(^)2875 4114 y Fd(b)2911 4126 y Fc(1)p 3091
4144 V 801 4147 2293 4 v 801 4164 V 799 4264 4 100 v
851 4234 a Fe(\(+)p Fd(;)14 b Fe(+\))p 1129 4264 V 99
w(sgn)o(\()p Fd(A)1395 4246 y Fc(1)1433 4234 y Fd(y)1474
4246 y Fc(1)1529 4234 y Fb(\000)k Fd(A)1674 4246 y Fc(1)1712
4234 y Fd(A)1774 4246 y Fc(2)1811 4234 y Fd(\032)p Fe(\))p
1935 4264 V 100 w Fd(A)2048 4246 y Fc(1)2086 4234 y Fd(A)2148
4246 y Fc(2)2185 4234 y Fb(j)p Fd(\032)p Fb(j)28 b Fe(is)f(minimal)p
2729 4264 V 100 w(sgn\()p Fd(y)2974 4246 y Fc(1)3011
4234 y Fe(\))p 3091 4264 V 801 4267 2293 4 v 799 4367
4 100 v 851 4337 a(\()p Fb(\000)p Fd(;)14 b Fb(\000)p
Fe(\))p 1129 4367 V 99 w(sgn)o(\()p Fd(A)1395 4349 y
Fc(1)1433 4337 y Fd(y)1474 4349 y Fc(1)1529 4337 y Fe(+)k
Fd(A)1674 4349 y Fc(1)1712 4337 y Fd(A)1774 4349 y Fc(2)1811
4337 y Fd(\032)p Fe(\))p 1935 4367 V 100 w Fd(A)2048
4349 y Fc(1)2086 4337 y Fd(A)2148 4349 y Fc(2)2185 4337
y Fb(j)p Fd(\032)p Fb(j)28 b Fe(is)f(minimal)p 2729 4367
V 100 w(sgn\()p Fd(y)2974 4349 y Fc(1)3011 4337 y Fe(\))p
3091 4367 V 801 4370 2293 4 v 799 4470 4 100 v 851 4440
a(\(+)p Fd(;)14 b Fb(\000)p Fe(\))p 1129 4470 V 131 w(sgn)o(\()p
Fd(A)1427 4452 y Fc(1)1465 4440 y Fd(y)1506 4452 y Fc(1)1562
4440 y Fe(+)k Fd(A)1707 4452 y Fc(2)1744 4440 y Fd(y)1785
4452 y Fc(2)1822 4440 y Fe(\))p 1935 4470 V 164 w Fd(A)2080
4452 y Fc(2)2118 4440 y Fb(j)p Fd(y)2182 4452 y Fc(2)2219
4440 y Fb(j)28 b Fe(is)f(minimal)p 2729 4470 V 132 w(sgn\()p
Fd(y)2974 4452 y Fc(1)3011 4440 y Fe(\))p 3091 4470 V
801 4473 2293 4 v 799 4573 4 100 v 851 4543 a(\()p Fb(\000)p
Fd(;)14 b Fe(+\))p 1129 4573 V 131 w(sgn)o(\()p Fd(A)1427
4555 y Fc(1)1465 4543 y Fd(y)1506 4555 y Fc(1)1562 4543
y Fb(\000)k Fd(A)1707 4555 y Fc(2)1744 4543 y Fd(y)1785
4555 y Fc(2)1822 4543 y Fe(\))p 1935 4573 V 164 w Fd(A)2080
4555 y Fc(2)2118 4543 y Fb(j)p Fd(y)2182 4555 y Fc(2)2219
4543 y Fb(j)28 b Fe(is)f(minimal)p 2729 4573 V 132 w(sgn\()p
Fd(y)2974 4555 y Fc(1)3011 4543 y Fe(\))p 3091 4573 V
801 4576 2293 4 v 639 4759 a(Th)n(us,)h(Equation)e(3)h(satis\014es)g
(condition)h(2)f(and)g(the)h(pro)r(of)f(is)h(complete.)1926
5506 y(2)p eop end
userdict /end-hook known{end-hook}if